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Orbital Decay of the Ultra-Hot Jupiter TOI-2109b: Tidal Constraints and Transit-Timing Analysis

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read TOI-2109b, the shortest-period ultra-hot Jupiter known, shows transit-timing variations consistent with a constant orbital period rather than rapid tidal decay.

desk verdict New TESS timing data give a solid upper limit on TOI-2109b's orbital decay, but the paper's young-versus-old star conclusion leans on an unquantified wave-breaking threshold. read the letter →

arxiv 2505.18941 v2 pith:RKB2BHQX submitted 2025-05-25 astro-ph.EP astro-ph.SR

Jaime A. Alvarado-Montes , Mario Sucerquia , Jorge I. Zuluaga , Christian Schwab This is my paper · ORCID
classification astro-ph.EPastro-ph.SR
keywords ultra-hotJupiterorbitaldecaytransittimingvariationstidaldissipationinertialwavesinternalgravitystellarqualityfactorTOI-2109b
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the ultra-hot Jupiter TOI-2109b—the shortest-period hot Jupiter known, with a 16-hour orbit—is not currently spiraling into its host star at a detectable rate. Re-analyzing transit timings from TESS, CHEOPS, and ground-based telescopes spanning 2020–2023, the authors find a best-fit period decay of −2.616 ± 1.285 ms/yr, consistent with a constant-period orbit and ruling out the 10–740 ms/yr range predicted when the planet was discovered. The key insight is that the efficiency of tidal dissipation in the F-type host star depends sharply on the star's age: inertial waves in the convective envelope dominate for a young star, while internal gravity waves in radiative regions would break and dissipate strongly only if the star is near its upper age limit. The data favor the young-star branch, implying a stellar tidal quality factor Q'_* > 3.7×$10^{7}$ and a decay slow enough that mid-transit times shift by less than about 10 seconds over three years. If correct, TOI-2109b becomes a testbed for quiet tidal evolution rather than a candidate for imminent orbital death.

What carries the argument

The engine of the argument is the coupled set of tidal evolution equations (constant time-lag model) with frequency-averaged tidal quality factors computed from two-layer interior models: inertial waves (IWs) in the convective envelope, internal gravity waves (IGWs) in radiative regions, and a viscoelastic solid core for the planet. The decisive element is the stellar-age dependence: internal gravity waves are efficiently damped only if the planet exceeds a critical mass $M_\mathrm{crit}$ that decreases with stellar age, so the same $\sim5\,M_\mathrm{J}$ planet produces either slow decay (young star, $Q'_{\star,\mathrm{IGW}} \approx 10^{8.5}$) or fast decay (old star, $Q'_{\star,\mathrm{IGW}} \propto (P_\mathrm{tide}/0.5\,\mathrm{d})^{8/3}$). The transit-timing measurements themselves are carried by a quadratic-ephemeris fit to 102 mid-transit times from TESS, CHEOPS, and ground-based follow-up, using a dedicated period-derivative fitting procedure.

What would settle it

Continue high-cadence transit timing of TOI-2109b for several more years. If the true decay were in the 10–740 ms/yr range, the cumulative mid-transit-time shift over the 2020–2028 baseline would reach tens of minutes to hours, vastly exceeding current uncertainties of roughly two minutes, so an absence of such drift would confirm the constant-period conclusion. Independently, a direct stellar age measurement (for example by asteroseismology or gyrochronology) would settle whether the star is young enough for the slow-decay branch to apply.

Watch

Extended reading notes

Core claim

The central claim is that transit-timing variations of TOI-2109b across four years of data favor a rather constant-period orbit, with a best-fit $\dot{P} = (-2.616 \pm 1.285)$ ms/yr at $3\sigma$, which excludes the fast-decay range of 10–740 ms/yr proposed in the discovery paper and supports a young host star with $Q'_\star > 3.7\times10^7$. In the authors' tidal evolution model, a young star dissipates tides mainly through inertial waves in the convective envelope, giving $\dot{P} \approx -4.2$ ms/yr, whereas an old star whose internal gravity waves reach the wave-breaking regime would decay at about $-1107$ ms/yr—a rate that would have produced easily visible shifts in the 2022 and 2024 TESS transits and is rejected by the data. The paper also shows that gravitational perturbations from a possible outer companion, stellar and planetary oblateness, and general-relativistic precession can each generate TTV signals that mimic or mask orbital decay, so those must be subtracted before attributing any trend to tides.

Load-bearing premise

The argument that the data single out a young host star rests on the wave-breaking threshold: the authors assume a 5-Jupiter-mass planet fully damps internal gravity waves only when the star is near its 2.65 Gyr upper age limit, because the critical mass for wave breaking from the adopted tidal model falls between 1 and 10 Jupiter masses at that age; if that threshold were different for a 1.45-solar-mass F star, the old-star scenario would not necessarily decay at the fast rate, and the timing data would no longer favor a young host.

Editorial extensions

If this is right

  • If the period is truly nearly constant, TOI-2109b is not on the verge of tidal disruption, and its 16-hour orbit can be used to probe stellar tidal quality factors near $Q'_\star \sim 10^7$ rather than a fast-decay endpoint.
  • The young-star scenario implies $Q'_\star > 2.3\times10^7$ from tidal modeling and $>3.7\times10^7$ from timing, values at the high end for F stars, which constrains how efficiently inertial waves dissipate in rapidly rotating convective envelopes.
  • Under the accepted decay rate, mid-transit times advance by less than about 10 seconds over three years, a signal detectable with high-cadence space photometry and a concrete target for future campaigns.
  • The demonstration that a possible outer companion, oblateness, and relativistic precession can produce TTV signals resembling decay means future analyses of ultra-short-period planets must model those effects before claiming orbital decay.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves stellar age as the dominant unknown; a precise age determination would break the young/old degeneracy and either confirm the slow decay or reopen the fast-decay scenario.
  • The assumption of a solid planetary core with rigidity derived from Jupiter-Io tidal interaction influences the planetary dissipation term; updated Jupiter interior models with a diluted core could shift the modeled $Q'_p$ and slightly alter the predicted $\dot{P}$.
  • If the suggested $\sim 0.2\,M_\mathrm{J}$ outer companion exists, its ~1–2 minute periodic TTV signal should be detectable in a few more CHEOPS or TESS sectors, offering a direct test independent of the decay question.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper studies the orbital evolution of the ultra-hot Jupiter TOI-2109b using a two-layer tidal model that includes inertial waves in the convective envelope and internal gravity waves in the radiative region, with stellar age as the key parameter. For a 'young' host star the model predicts a slow period decay of approximately -4 ms/yr, while for an 'old' host star (t_age = 2.65 Gyr) it predicts a much faster decay of about -1100 ms/yr. The authors combine TESS data from three sectors (including new 20-s cadence data from Sector 79), CHEOPS transit times from the literature, and ground-based light curves to perform a TTV analysis with the PdotQuest code. They find a best-fit period decay of Pdot_OBSV = (-2.616 ± 1.285) ms/yr under a 3-sigma rejection scheme, which rules out the high end of the 10-740 ms/yr range suggested by Wong et al. (2021) and yields a 95% lower limit of Q'_* > 3.7 × 10^7. The authors interpret this as support for a young host star and a constant-period orbit, and they also simulate TTV contributions from an outer companion, stellar/planetary oblateness, and general relativity to aid interpretation.

Significance. The observational TTV result is a solid contribution: it incorporates new TESS 20-s cadence data, re-reduces earlier TESS and ground-based transits, and reports a consistent small period decay under two sigma-clipping schemes. This is a genuine, model-independent timing constraint that tightens the lower limit on Q'_* and rules out the fast-decay end of previous predictions. The paper also makes its timing data and reduction code publicly available, which supports reproducibility. If the young-star interpretation holds, the result implies that TOI-2109b is not currently spiraling into its host star at an observable rate and that stellar age is a controlling factor in tidal dissipation efficiency. The theoretical tidal modeling, however, rests on two under-specified inputs—the Barker (2020) critical-mass threshold and the scaling of the two-layer inertial-wave model—so the central age interpretation is less secure than the timing measurement itself.

major comments (3)
  1. [§4.2 and Table 1] The division into 'young' and 'old' host-star scenarios relies on an unquantified critical-mass threshold from Barker (2020). The authors state that at t_age = 2.65 Gyr (the 1-sigma upper age limit in Table 1) M_crit lies between 1 and 10 M_J, so a ~5 M_J planet fully damps IGWs; they do not quote M_crit itself nor its dependence on stellar mass and age. If M_crit exceeds 5 M_J at this age, or if the true age is below 2.65 Gyr, the 'old' star reverts to Q'_IGW ≈ 10^8.5 and Pdot_TIDE ≈ 4 ms/yr, making it observationally indistinguishable from the 'young' case. Since the abstract's claim that TTVs 'support a young host star' depends entirely on this binary threshold, the authors should compute or quote M_crit from Barker (2020) and show how it varies across the allowed age range, and present the old-star prediction as a conditional scenario rather than a fixed alternative.
  2. [§3.1 and §4.1] The two-layer inertial-wave model is said to underpredict dissipation in F-type stars by 1-2 orders of magnitude, and the authors account for the difference by using Barker (2020) to scale Q'_*, but no numerical scale factor, equation, or methodology is provided. As a result, the quoted Pdot_TIDE = (-4.186 ± 0.797) ms/yr for the young-star scenario is not reproducible, and its uncertainty almost certainly understates the model error from the unspecified scaling. This matters because the central comparison in Section 5.3 between Pdot_TIDE and Pdot_OBSV = (-2.616 ± 1.285) ms/yr is used to support the young-star interpretation; a factor of a few in the scaling would change the theoretical prediction by an order of magnitude and could spoil the agreement.
  3. [§5.3] The conversion from the fitted Pdot_OBSV to the headline lower limit Q'_*,OBSV > 3.7 × 10^7 is not shown. Unlike Section 4.1, where the Goldreich & Soter relation and adopted stellar/planetary parameters are described, Section 5.3 simply states the result. The authors should present the formula used to convert a measured period derivative into Q'_* and list the assumed values of M_p, R_*, a, and the stellar moment of inertia, so that the reader can verify the one-sided 95% lower limit. This is a central quantitative claim of the paper.
minor comments (5)
  1. [§5.3 and §6] There are a few typographical errors: 'With a a cadence' in Section 5.3 and 'evolutionaryS timescales' in Section 6.
  2. [§5.3] The statement that the result 'rules out any Pdot > 10 ms/yr' is imprecise. The 3-sigma interval on Pdot is approximately [-6.5, 1.3] ms/yr, so a decay rate of 10 ms/yr is excluded at about 5.7 sigma; the formal significance should be stated instead.
  3. [§5.1 and §5.2] When combining TESS, CHEOPS, and heterogeneous ground-based data, the analysis does not quantify correlated red noise or possible systematic offsets between instruments. The reported uncertainties on Pdot would be more robust if a jitter term or per-instrument offset were included; at least a brief discussion of this limitation should be added.
  4. [Figure 9] The two sigma-rejection fits use different samples (53 vs 102 transits); it would aid interpretation to plot both data sets and the best quadratic curves with residuals in a single panel, in addition to the TTV plots shown.
  5. [§5.4] The simulated TTV amplitudes from the companion, oblateness, and general relativity are presented without a quantitative comparison to the observed TTV residuals. Even a simple chi-square or amplitude comparison would clarify whether these effects are consistent with the data or are merely illustrative.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the observed period decay is measured independently of the tidal model, and the theoretical decay rates are forward-model outputs compared with, not fitted to, the TTV data.

full rationale

The paper's central test is a genuine model-vs-data comparison. The observed decay rate, Pdot_OBSV = (-2.616 ± 1.285) ms/yr, is obtained by fitting a quadratic ephemeris to 102 transit times from TESS, CHEOPS, and ground-based observations (Section 5.3, Table 4). This fit involves no tidal parameters. The theoretical decay rates for the young and old stellar scenarios are obtained by integrating the tidal evolution equations with quality factors computed from structural inputs and external tidal-dissipation prescriptions (Sections 3 and 4). The young-star value Pdot_TIDE = (-4.186 ± 0.797) ms/yr and the old-star value Pdot_TIDE = (-1107 ± 648) ms/yr follow from those forward simulations and are not constructed from the measured TTVs. The age discrimination does depend on the binary M_crit threshold from Barker (2020), but that is an external published calculation, not a self-citation, and the paper itself flags the old-star scenario as uncertain ('should be taken with a grain of salt', Section 6). The self-citations in the paper (Alvarado-Montes 2022; Alvarado-Montes et al. 2021) concern the choice of tidal evolution code and a comparison of stellar spin-up; they are not used to define the measured quantity or to forbid alternative interpretations. The TTV analysis also explicitly considers non-tidal sources of transit-timing variation in Section 5.4. Therefore, no claimed prediction reduces by construction to its inputs, and no load-bearing argument reduces to a self-citation. Scientific concerns about the M_crit threshold or the constant-Q' assumption are modeling uncertainties, not circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 1 invented entities

The central theoretical prediction (Pdot_TIDE) rests on a chain of literature models: constant-lag equilibrium tides, frequency-averaged IW dissipation, and Barker (2020) scalings for IGW dissipation. The most fragile inputs are the undisclosed Barker scaling for Q'_IW and the binary M_crit switch for IGW wave breaking. The observational Pdot_OBSV is independent of these choices, which is why the ruling out of fast decay is more robust than the young-star interpretation.

free parameters (4)
  • Stellar interior aspect ratios alpha_* and beta_* = Not explicitly quoted in text; adopted from Gallet et al. (2017) for M* ~ 1.45 M_sun (Figure 3 shows the allowed range)
    These two structural ratios control the inertial-wave tidal quality factor Q'_*,IW through Eq. (14). The paper does not fit them but chooses literature values, and the predicted Pdot_TIDE depends on them.
  • Barker (2020) scaling factor for Q'_*,IW = Not stated
    The two-layer model is said to underpredict IW dissipation in F stars by 1-2 orders of magnitude, and Q'_* is 'scaled' to Barker's realistic models, but no scaling formula or numeric factor is given. This is effectively an undisclosed free parameter in the theoretical Pdot_TIDE.
  • Normalization C in Q'_*,IGW = C (P_tide/0.5 d)^(8/3) = 3
    C is adopted from Barker (2020) and set to 3 for TOI-2109; changing C by a factor of 2 changes Pdot_TIDE by ~34% in the old-star scenario.
  • Planet core rigidity R = 4.46e10 Pa
    Taken from Jupiter-Io tidal interaction (Lainey et al. 2012); controls viscoelastic dissipation in the planet's core via Eq. (15), with negligible effect on the stellar-driven orbital decay.
assumptions (5)
  • domain assumption Constant tidal lag-time model (Hut 1981) with Q' = 1/(2 n_p tau) and dominant tidal frequency omega ~ 2 n_p
    Adopted in Section 2 to close the tidal evolution equations; Q' is assumed independent of frequency, which is a known simplification.
  • domain assumption Frequency-averaged inertial-wave dissipation formalism (Ogilvie 2013) is representative of the true IW dissipation in TOI-2109
    Used in Section 3.1; the authors acknowledge that specific-frequency IW dissipation is uncertain by 2-3 orders of magnitude and neglect non-linear/magnetic effects.
  • domain assumption Internal gravity wave dissipation follows Barker (2020): Q'_*,IGW ~ 10^8.5 and Q'_*,IGW ∝ (P_tide/0.5 d)^(8/3) when the planet mass exceeds M_crit
    Applied in Sections 3.2 and 4.2. The wave-breaking criterion M_crit is taken from fig. 9 of Barker (2020) and is not recomputed here; this is the binary switch between the 'young' and 'old' scenarios.
  • domain assumption Spin-orbit alignment and negligible obliquity
    Assumed in Section 2 and matched to the measured sky-projected obliquity lambda = 1.7 +/- 1.7 deg (Wong et al. 2021).
  • domain assumption Stellar rotation period P_rot = 1.05 d (from v sin i and assumed inclination) and no core-envelope decoupling
    Adopted from Wong et al. (2021); the rotation period sets the boundary for IW excitation (P_orb >= P_rot/2) and the sign of the tidal torque.
invented entities (1)
  • Hypothetical outer companion TOI-2109c (0.2 M_J, P ~ 1.125 d, e = 0.05)
    purpose: Used in REBOUNDx simulations (Section 5.4) to demonstrate that a close companion can generate 1-2 minute TTVs that could mimic or contaminate an orbital-decay signal.
    No detection is claimed; the companion is presented as a plausible perturber motivated by Harre et al. (2024). It is an invented entity for the purpose of the contamination test.

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Cite this review

Pith. "Pith review of Orbital Decay of the Ultra-Hot Jupiter TOI-2109b: Tidal Constraints and Transit-Timing Analysis." pith.science (2026). https://pith.science/paper/RKB2BHQX

@misc{pith2026250518941,
  author       = {Pith},
  title        = {Pith review of: Orbital Decay of the Ultra-Hot Jupiter TOI-2109b: Tidal Constraints and Transit-Timing Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RKB2BHQX}},
  note         = {Machine review of arXiv:2505.18941}
}
abstract

TOI-2109b is the ultra-hot Jupiter with the shortest orbital period ($\sim16\,$hr) yet discovered. At this close distance, strong tidal interactions can produce a significant exchange of angular momentum with the star. Since the orbital period of this planet is shorter than the stellar rotation period, TOI-2109b may be an optimal candidate for studying orbital decay. This process depends on how efficiently the star and the planet dissipate energy, due mainly to interior mechanisms that are poorly constrained in exoplanet systems. In this work, we study for the first time the tidal evolution of TOI-2109b under a formalism of inertial waves (IWs) in convective envelopes and internal gravity waves (IGWs) in stellar radiative regions. We find that uncertainties in the age of TOI-2109 ($t_\mathrm{\star, age}$) significantly affect the rate of orbital evolution, as IWs and IGWs interact differently depending on $t_\mathrm{\star, age}$. For an 'old' host star, we find that TOI-2109b would undergo fast orbital decay. Conversely, if TOI-2109b orbits a 'young' host star, a rather slow decay rate for $Q_\star'>2.3\times10^7$ would suggest a constant-period orbit. Our calculated mid-transit times and transit-timing variations (TTVs) support a 'young' host star with $Q_\star'>3.7\times10^7$, suggesting a decay rate $\dot{P}\sim4\,$ms yr$^{-1}$ that could lead to mid-transit-time shifts $\lesssim10\,$s over three years. Orbital decay and other TTV-inducing effects will be confirmed or ruled out with future higher-quality timing data. The results presented here aim at constraining the current modeling of tides and TTVs for TOI-2109b, helping us further understand light-curve changes associated to the long-term evolution of ultra-short-period planets.

Figures

Figures reproduced from arXiv: 2505.18941 by the authors.

Figure 1
Figure 1. Distribution of USP Jupiter-like planets (𝑃orb < 1 d; J. N. Winn et al. 2018). Colors represent equilibrium temperatures. Data extracted from the NASA Exoplanet Archive (2025). Ogilvie 2013; S. Mathis 2015; E. Bolmont & S. Mathis 2016; F. Gallet et al. 2017; M. Benbakoura et al. 2019), and the excitation of internal gravity waves (IGWs) via tidal forcing in stellar radiative regions (A. J. Barker & G. I. Ogilvie 201… view at source ↗
Figure 2
Figure 2. Schematic depiction of the TOI-2109b system, illustrating the primary physical and orbital parameters that describe the evolution of the system in response to tidal interactions between the planet and its host star. of 𝑄 ′ is complicated owing to its dependence on the tidal frequency 𝜔 (see, e.g., G. I. Ogilvie & D. N. C. Lin 2007), which is a result of the intricate internal mechanisms whereby interacting rotating … view at source ↗
Figure 3
Figure 3. Tidal quality factor 𝑄 ′ ★,IW as a function of the stellar aspect ratios 𝛼★ and 𝛽★ of TOI-2109. 𝑃orb ≥ 𝑃rot,★ 2 so that IWs and IGWs act together, and 2) when the planet reaches inner positions where IWs are no longer excited (i.e., 𝑃orb ≱ 𝑃rot,★ 2 ), leaving IGWs as the only active dissipation mechanism for shorter orbital periods. Tidal dis￾sipation due to IGWs in radiative regions strongly depends on the orbital/… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: shows the evolution of the semi-major axis for different values of 𝑄 ′ ★, IW, where tidal dissipation arises mostly from excited IWs. From these tidal simulations we calculate the decay rate of the orbital period as 𝑃¤ TIDE = (−4.186 ± 0.797) ms yr−1 at 3𝜎. Using the f…
Figure 5
Figure 5. Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: TESS light curve of TOI-2109b. The groups of red points are the transit intervals, which are centered on the predicted transit times and extend for four transit durations. TESS data from Sector 52 with a two-minute cadence [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Folded light curve of TOI-2109b using the data of [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Individual transits extracted from [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: TTVs of TOI-2109b calculated with PdotQuest, from an MCMC fit using a quadratic model. The fit is performed for a 1-sigma (upper panel) and 3-sigma (lower panel) rejection areas. (i.e., the blue shaded regions) [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: TTVs of TOI-2109b under different dynamical scenarios. The green points represent TTVs resulting from Newtonian gravitational interactions with an additional planetary companion (planet c, 𝑃𝑐 ≈ 1.125 d, 𝑒𝑐 = 0.05). The orange points depict the secular TTV trend as a r…
Figure 11
Figure 11. Figure 11: Advance in mid-transit times of TOI-2109b measured in human timescales. This is for the scenario of a ‘young’ host star. Kepler-1658b (S. Vissapragada et al. 2022), can be a valuable method to further study the possibility of orbital decay in this system. Our TTV anal…

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Works this paper leans on

115 extracted references · 14 canonical work pages

  1. [1]

    R., Jackson, B., Sickafoose, A

    Adams, E. R., Jackson, B., Sickafoose, A. A., et al. 2024, PSJ, 5, 163, doi: 10.3847/PSJ/ad3e80

    doi:10.3847/psj/ad3e80 2024

  2. [2]

    Akinsanmi, B., Barros, S. C. C., Santos, N. C., et al. 2019, A&A, 621, A117, doi: 10.1051/0004-6361/201834215

    doi:10.1051/0004-6361/201834215 2019

  3. [3]

    Akinsanmi, B., Barros, S. C. C., Lendl, M., et al. 2024, A&A, 685, A63, doi: 10.1051/0004-6361/202348502

    doi:10.1051/0004-6361/202348502 2024

  4. [4]

    Alexander, M. E. 1973, Ap&SS, 23, 459, doi: 10.1007/BF00645172

    doi:10.1007/bf00645172 1973

  5. [5]

    B., Patra, K

    Alvarado, E., Bostow, K. B., Patra, K. C., et al. 2024, MNRAS, 534, 800, doi: 10.1093/mnras/stae2062

    doi:10.1093/mnras/stae2062 2024

  6. [6]

    Alvarado-Montes, J. A. 2022, MNRAS, 517, 2831, doi: 10.1093/mnras/stac2741

    doi:10.1093/mnras/stac2741 2022

  7. [7]

    A., & García-Carmona, C

    Alvarado-Montes, J. A., & García-Carmona, C. 2019, MNRAS, 486, 3963, doi: 10.1093/mnras/stz1081

    doi:10.1093/mnras/stz1081 2019

  8. [8]

    A., Sucerquia, M., García-Carmona, C., et al

    Alvarado-Montes, J. A., Sucerquia, M., García-Carmona, C., et al. 2021, MNRAS, 506, 2247, doi: 10.1093/mnras/stab1081

    doi:10.1093/mnras/stab1081 2021

Show all 115 references
  1. [9]

    2019, MNRAS, 482, 1872, doi: 10.1093/mnras/sty2805

    Bailey, A., & Goodman, J. 2019, MNRAS, 482, 1872, doi: 10.1093/mnras/sty2805

    2019 doi

  2. [11]

    Barker, A. J. 2016, MNRAS, 459, 939, doi: 10.1093/mnras/stw702

    2016 doi

  3. [12]

    Barker, A. J. 2020, MNRAS, 498, 2270, doi: 10.1093/mnras/staa2405

    2020 doi

  4. [13]

    J., Efroimsky, M., Makarov, V

    Barker, A. J., Efroimsky, M., Makarov, V. V., & Veras, D. 2024, MNRAS, 527, 5131, doi: 10.1093/mnras/stad3530

    2024 doi

  5. [14]

    J., & Ogilvie, G

    Barker, A. J., & Ogilvie, G. I. 2009, MNRAS, 395, 2268, doi: 10.1111/j.1365-2966.2009.14694.x

    2009

  6. [15]

    J., & Ogilvie, G

    Barker, A. J., & Ogilvie, G. I. 2010, MNRAS, 404, 1849, doi: 10.1111/j.1365-2966.2010.16400.x

    2010

  7. [16]

    Barros, S. C. C., Akinsanmi, B., Boué, G., et al. 2022, A&A, 657, A52, doi: 10.1051/0004-6361/202142196

    2022 doi

  8. [17]

    2019, A&A, 621, A124, doi: 10.1051/0004-6361/201833314

    Mathis, S. 2019, A&A, 621, A124, doi: 10.1051/0004-6361/201833314

    2019 doi

  9. [18]

    P., & Parthasarathy, K

    Biswas, S., Bisht, D., Jiang, I.-G., Sariya, D. P., & Parthasarathy, K. 2024, AJ, 168, 176, doi: 10.3847/1538-3881/ad6d66

    2024 doi

  10. [19]

    2016, Celestial Mechanics and Dynamical Astronomy, 126, 275, doi: 10.1007/s10569-016-9690-3

    Bolmont, E., & Mathis, S. 2016, Celestial Mechanics and Dynamical Astronomy, 126, 275, doi: 10.1007/s10569-016-9690-3

    2016 doi

  11. [20]

    G., Winn, J

    Bouma, L. G., Winn, J. N., Baxter, C., et al. 2019, AJ, 157, 217, doi: 10.3847/1538-3881/ab189f

    2019 doi

  12. [21]

    2022, A&A, 659, L4, doi: 10.1051/0004-6361/202243082

    Brandeker, A., Heng, K., Lendl, M., et al. 2022, A&A, 659, L4, doi: 10.1051/0004-6361/202243082

    2022 doi

  13. [22]

    2011, MNRAS, 415, 605, doi: 10.1111/j.1365-2966.2011.18729.x

    Smalley, B. 2011, MNRAS, 415, 605, doi: 10.1111/j.1365-2966.2011.18729.x

    2011

  14. [23]

    M., Baliber, N., Bianco, F

    Brown, T. M., Baliber, N., Bianco, F. B., et al. 2013, PASP, 125, 1031, doi: 10.1086/673168

    2013 doi

  15. [24]

    A., Tenenbaum, P., Twicken, J

    Caldwell, D. A., Tenenbaum, P., Twicken, J. D., et al. 2020, Research Notes of the American Astronomical Society, 4, 201, doi: 10.3847/2515-5172/abc9b3

    2020 doi

  16. [25]

    J., Kashyap, V

    Cohen, O., Drake, J. J., Kashyap, V. L., Sokolov, I. V., & Gombosi, T. I. 2010, ApJL, 723, L64, doi: 10.1088/2041-8205/723/1/L64 Collier Cameron, A., & Jardine, M. 2018, MNRAS, 476, 2542, doi: 10.1093/mnras/sty292 Collier Cameron, A., & Li, J. 1994, MNRAS, 269, 1099, doi: 10.1...

    2010 doi

  17. [26]

    2025, arXiv e-prints, arXiv:2504.15757

    Cont, D., Nortmann, L., Lesjak, F., et al. 2025, arXiv e-prints, arXiv:2504.15757. https://arxiv.org/abs/2504.15757

    2025 arXiv

  18. [27]

    I., & Johnson, J

    Dawson, R. I., & Johnson, J. A. 2018, ARA&A, 56, 175, doi: 10.1146/annurev-astro-081817-051853 17

    2018 doi

  19. [28]

    2023, Nature, 617, 55, doi: 10.1038/s41586-023-05842-x

    De, K., MacLeod, M., Karambelkar, V., et al. 2023, Nature, 617, 55, doi: 10.1038/s41586-023-05842-x

    2023 doi

  20. [29]

    M., et al

    Delrez, L., Santerne, A., Almenara, J. M., et al. 2016, MNRAS, 458, 4025, doi: 10.1093/mnras/stw522

    2016 doi

  21. [30]

    D., de Vries, N

    Duguid, C. D., de Vries, N. B., Lecoanet, D., & Barker, A. J. 2024, ApJL, 966, L14, doi: 10.3847/2041-8213/ad3c40

    2024 doi

  22. [31]

    2012, ApJ, 746, 150, doi: 10.1088/0004-637X/746/2/150

    Efroimsky, M. 2012, ApJ, 746, 150, doi: 10.1088/0004-637X/746/2/150

    2012 doi

  23. [32]

    Essick, R., & Weinberg, N. N. 2016, ApJ, 816, 18, doi: 10.3847/0004-637X/816/1/18

    2016 doi

  24. [33]

    2023, A&A, 669, A2, doi: 10.1051/0004-6361/202243621

    Fellay, L., Pezzotti, C., Buldgen, G., Eggenberger, P., & Bolmont, E. 2023, A&A, 669, A2, doi: 10.1051/0004-6361/202243621

    2023 doi

  25. [34]

    J., & Matt, S

    Finley, A. J., & Matt, S. P. 2017, ApJ, 845, 46, doi: 10.3847/1538-4357/aa7fb9

    2017 doi

  26. [35]

    2017, A&A, 604, A112, doi: 10.1051/0004-6361/201730661

    Gallet, F., Bolmont, E., Mathis, S., Charbonnel, C., & Amard, L. 2017, A&A, 604, A112, doi: 10.1051/0004-6361/201730661

    2017 doi

  27. [36]

    S., Stassun, K

    Gaudi, B. S., Stassun, K. G., Collins, K. A., et al. 2017, Nature, 546, 514, doi: 10.1038/nature22392

    2017 doi

  28. [37]

    1966, icarus, 5, 375, doi: 10.1016/0019-1035(66)90051-0

    Goldreich, P., & Soter, S. 1966, icarus, 5, 375, doi: 10.1016/0019-1035(66)90051-0

    1966 doi

  29. [38]

    V., & Wang, S

    Goyal, A. V., & Wang, S. 2025, AJ, 169, 191, doi: 10.3847/1538-3881/adb487

    2025 doi

  30. [39]

    Gu, P.-G., Lin, D. N. C., & Bodenheimer, P. H. 2003, ApJ, 588, 509, doi: 10.1086/373920

    2003 doi

  31. [40]

    2014, A&A, 566, L9, doi: 10.1051/0004-6361/201424010

    Guenel, M., Mathis, S., & Remus, F. 2014, A&A, 566, L9, doi: 10.1051/0004-6361/201424010

    2014 doi

  32. [41]

    R., Edwards, B., & Boley, A

    Hagey, S. R., Edwards, B., & Boley, A. C. 2022, AJ, 164, 220, doi: 10.3847/1538-3881/ac959a

    2022 doi

  33. [42]

    H., & Schlaufman, K

    Hamer, J. H., & Schlaufman, K. C. 2020, AJ, 160, 138, doi: 10.3847/1538-3881/aba74f

    2020 doi

  34. [43]

    Harre, J.-V., & Smith, A. M. S. 2023, Universe, 9, 506, doi: 10.3390/universe9120506

    2023 doi

  35. [44]

    V., Smith, A

    Harre, J. V., Smith, A. M. S., Barros, S. C. C., et al. 2024, A&A, 692, A254, doi: 10.1051/0004-6361/202451068

    2024 doi

  36. [45]

    2022, MNRAS, 511, 3133, doi: 10.1093/mnras/stac169

    Hou, Q., & Wei, X. 2022, MNRAS, 511, 3133, doi: 10.1093/mnras/stac169

    2022 doi

  37. [46]

    W., Marcy, G

    Howard, A. W., Marcy, G. W., Bryson, S. T., et al. 2012, ApJS, 201, 15, doi: 10.1088/0067-0049/201/2/15

    2012 doi

  38. [47]

    2020, A&A, 635, A24, doi: 10.1051/0004-6361/201936325

    Hoyer, S., Guterman, P., Demangeon, O., et al. 2020, A&A, 635, A24, doi: 10.1051/0004-6361/201936325

    2020 doi

  39. [48]

    B., Papaloizou, J

    Ivanov, P. B., Papaloizou, J. C. B., & Chernov, S. V. 2013, MNRAS, 432, 2339, doi: 10.1093/mnras/stt595

    2013 doi

  40. [49]

    S., & Winn, J

    Ivshina, E. S., & Winn, J. N. 2022, ApJS, 259, 62, doi: 10.3847/1538-4365/ac545b

    2022 doi

  41. [50]

    2016, Celestial Mechanics and Dynamical Astronomy, 126, 227, doi: 10.1007/s10569-016-9704-1

    Jackson, B., Jensen, E., Peacock, S., Arras, P., & Penev, K. 2016, Celestial Mechanics and Dynamical Astronomy, 126, 227, doi: 10.1007/s10569-016-9704-1

    2016 doi

  42. [51]

    P., Güdel, M., Lüftinger, T., Toth, G., & Brott, I

    Johnstone, C. P., Güdel, M., Lüftinger, T., Toth, G., & Brott, I. 2015, A&A, 577, A27, doi: 10.1051/0004-6361/201425300

    2015 doi

  43. [52]

    M., Demory, B

    Jones, K., Morris, B. M., Demory, B. O., et al. 2022, A&A, 666, A118, doi: 10.1051/0004-6361/202243823

    2022 doi

  44. [53]

    1960, Figures of Equilibrium of Celestial Bodies: With Emphasis on Problems of Motion of Artificial Satellites (Madison, WI: University of Wisconsin Press), 135

    Kopal, Z. 1960, Figures of Equilibrium of Celestial Bodies: With Emphasis on Problems of Motion of Artificial Satellites (Madison, WI: University of Wisconsin Press), 135

    1960

  45. [54]

    Kotorashvili, K., & Blackman, E. G. 2024, arXiv e-prints, arXiv:2411.17916. https://arxiv.org/abs/2411.17916

    2024

  46. [55]

    2012, ApJ, 752, 14, doi: 10.1088/0004-637X/752/1/14

    Lainey, V., Karatekin, Ö., Desmars, J., et al. 2012, ApJ, 752, 14, doi: 10.1088/0004-637X/752/1/14

    2012 doi

  47. [56]

    Lanza, A. F. 2010, A&A, 512, A77, doi: 10.1051/0004-6361/200912789

    2010 doi

  48. [57]

    F., Damiani, C., & Gandolfi, D

    Lanza, A. F., Damiani, C., & Gandolfi, D. 2011, A&A, 529, A50, doi: 10.1051/0004-6361/201016144

    2011 doi

  49. [58]

    Lazovik, Y. A. 2021, MNRAS, 508, 3408, doi: 10.1093/mnras/stab2768

    2021 doi

  50. [59]

    2010, A&A, 516, A64, doi: 10.1051/0004-6361/201014337

    Leconte, J., Chabrier, G., Baraffe, I., & Levrard, B. 2010, A&A, 516, A64, doi: 10.1051/0004-6361/201014337

    2010 doi

  51. [60]

    2024, A&A, 686, A84, doi: 10.1051/0004-6361/202348363

    Leonardi, P., Nascimbeni, V., Granata, V., et al. 2024, A&A, 686, A84, doi: 10.1051/0004-6361/202348363

    2024 doi

  52. [61]

    2009, ApJL, 692, L9, doi: 10.1088/0004-637X/692/1/L9 Lightkurve Collaboration, Cardoso, J

    Levrard, B., Winisdoerffer, C., & Chabrier, G. 2009, ApJL, 692, L9, doi: 10.1088/0004-637X/692/1/L9 Lightkurve Collaboration, Cardoso, J. V. d. M., Hedges, C., et al. 2018,, Astrophysics Source Code Library http://ascl.net/1812.013

    2009 doi

  53. [62]

    Lin, Y., & Ogilvie, G. I. 2018, MNRAS, 474, 1644, doi: 10.1093/mnras/stx2764

    2018 doi

  54. [63]

    Love, A. E. H. 1927, A Treatise on the Mathematical Theory of

    1927

  55. [64]

    2021, ApJ, 918, 16, doi: 10.3847/1538-4357/ac088e

    Ma, L., & Fuller, J. 2021, ApJ, 918, 16, doi: 10.3847/1538-4357/ac088e

    2021 doi

  56. [65]

    2021, A&A, 656, A88, doi: 10.1051/0004-6361/202142424

    Maciejewski, G., Fernández, M., Aceituno, F., et al. 2021, A&A, 656, A88, doi: 10.1051/0004-6361/202142424

    2021 doi

  57. [66]

    2016, A&A, 588, L6, doi: 10.1051/0004-6361/201628312

    Maciejewski, G., Dimitrov, D., Fernández, M., et al. 2016, A&A, 588, L6, doi: 10.1051/0004-6361/201628312

    2016 doi

  58. [67]

    2002, ApJL, 580, L171, doi: 10.1086/345520

    Mandel, K., & Agol, E. 2002, ApJL, 580, L171, doi: 10.1086/345520

    2002 doi

  59. [68]

    2015, A&A, 580, L3, doi: 10.1051/0004-6361/201526472

    Mathis, S. 2015, A&A, 580, L3, doi: 10.1051/0004-6361/201526472

    2015 doi

  60. [69]

    1995, Nature, 378, 355, doi: 10.1038/378355a0

    Mayor, M., & Queloz, D. 1995, Nature, 378, 355, doi: 10.1038/378355a0

    1995 doi

  61. [70]

    2019, ApJ, 886, 72, doi: 10.3847/1538-4357/ab4c3f Mol Lous, M., & Miguel, Y

    Millholland, S. 2019, ApJ, 886, 72, doi: 10.3847/1538-4357/ab4c3f Mol Lous, M., & Miguel, Y. 2020, MNRAS, 495, 2994, doi: 10.1093/mnras/staa1405 Müller, S., Helled, R., & Cumming, A. 2020, A&A, 638, A121, doi: 10.1051/0004-6361/201937376

    2019 doi

  62. [71]

    D., & Dermott, S

    Murray, C. D., & Dermott, S. F. 2000, Solar System Dynamics (New York: Cambridge Univ. Press) NASA Exoplanet Archive. 2025,, Version: 2025-04-27 21:00 NExScI-Caltech/IPAC, doi: 10.26133/NEA12 18Jaime A. Alvarado-Montes et al

    2000 doi

  63. [72]

    E., Rodriguez, J

    Oberst, T. E., Rodriguez, J. E., Colón, K. D., et al. 2017, AJ, 153, 97, doi: 10.3847/1538-3881/153/3/97

    2017 doi

  64. [73]

    Ogilvie, G. I. 2013, MNRAS, 429, 613, doi: 10.1093/mnras/sts362

    2013 doi

  65. [74]

    I., & Lin, D

    Ogilvie, G. I., & Lin, D. N. C. 2007, ApJ, 661, 1180, doi: 10.1086/515435

    2007 doi

  66. [75]

    M., Brewer, J

    Oh, S., Price-Whelan, A. M., Brewer, J. M., et al. 2018, ApJ, 854, 138, doi: 10.3847/1538-4357/aaab4d

    2018 doi

  67. [76]

    R., Bean, J

    Parmentier, V., Line, M. R., Bean, J. L., et al. 2018, A&A, 617, A110, doi: 10.1051/0004-6361/201833059

    2018 doi

  68. [77]

    2015, MNRAS, 450, 3233, doi: 10.1093/mnras/stv894

    Parviainen, H. 2015, MNRAS, 450, 3233, doi: 10.1093/mnras/stv894

    2015 doi

  69. [78]

    C., Winn, J

    Patra, K. C., Winn, J. N., Holman, M. J., et al. 2017, AJ, 154, 4, doi: 10.3847/1538-3881/aa6d75

    2017 doi

  70. [79]

    C., Winn, J

    Patra, K. C., Winn, J. N., Holman, M. J., et al. 2020, AJ, 159, 150, doi: 10.3847/1538-3881/ab7374

    2020 doi

  71. [80]

    G., Winn, J

    Penev, K., Bouma, L. G., Winn, J. N., & Hartman, J. D. 2018, AJ, 155, 165, doi: 10.3847/1538-3881/aaaf71

    2018 doi

  72. [81]

    D., Bakos, G

    Penev, K., Hartman, J. D., Bakos, G. Á., et al. 2016, AJ, 152, 127, doi: 10.3847/0004-6256/152/5/127

    2016 doi

  73. [82]

    2020, MNRAS, 491, 1243, doi: 10.1093/mnras/stz3034

    Petrucci, R., Jofré, E., Gómez Maqueo Chew, Y., et al. 2020, MNRAS, 491, 1243, doi: 10.1093/mnras/stz3034

    2020 doi

  74. [83]

    L., Skillen, I., Collier Cameron, A., et al

    Pollacco, D. L., Skillen, I., Collier Cameron, A., et al. 2006, PASP, 118, 1407, doi: 10.1086/508556

    2006 doi

  75. [84]

    Rein, H., & Liu, S. F. 2012, A&A, 537, A128, doi: 10.1051/0004-6361/201118085

    2012 doi

  76. [85]

    2015, MNRAS, 452, 376, doi: 10.1093/mnras/stv1257

    Rein, H., & Tamayo, D. 2015, MNRAS, 452, 376, doi: 10.1093/mnras/stv1257

    2015 doi

  77. [86]

    R., Winn, J

    Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015, JATIS, 1, 014003, doi: 10.1117/1.JATIS.1.1.014003

    2015 doi

  78. [87]

    2010, Journal of Fluid Mechanics, 643, 363, doi: 10.1017/S002211200999214X

    Rieutord, M., & Valdettaro, L. 2010, Journal of Fluid Mechanics, 643, 363, doi: 10.1017/S002211200999214X

    2010 doi

  79. [88]

    1849, Acad

    Roche, E. 1849, Acad. Montpellier, 1, 243 Rosário, N. M., Barros, S. C. C., Demangeon, O. D. S., & Santos, N. C. 2022, A&A, 668, A114, doi: 10.1051/0004-6361/202244513

    2022 doi

  80. [89]

    B., & Grishin, E

    Rozner, M., Glanz, H., Perets, H. B., & Grishin, E. 2022, ApJ, 931, 10, doi: 10.3847/1538-4357/ac6808

    2022 doi

  81. [90]

    2011, A&A, 532, A6, doi: 10.1051/0004-6361/201116594

    Sanz-Forcada, J., Micela, G., Ribas, I., et al. 2011, A&A, 532, A6, doi: 10.1051/0004-6361/201116594

    2011 doi

  82. [91]

    G., Oelkers, R

    Stassun, K. G., Oelkers, R. J., Pepper, J., et al. 2018, AJ, 156, 102, doi: 10.3847/1538-3881/aad050

    2018 doi

  83. [92]

    P., Naoz, S., & Gaudi, B

    Stephan, A. P., Naoz, S., & Gaudi, B. S. 2018, AJ, 156, 128, doi: 10.3847/1538-3881/aad6e5

    2018 doi

  84. [93]

    2025, A&A, 694, L8, doi: 10.1051/0004-6361/202452968

    Sucerquia, M., & Cuello, N. 2025, A&A, 694, L8, doi: 10.1051/0004-6361/202452968

    2025 doi

  85. [94]

    Tamayo, D., Rein, H., Shi, P., & Hernandez, D. M. 2020, MNRAS, 491, 2885, doi: 10.1093/mnras/stz2870

    2020 doi

  86. [95]

    Tokuno, T., Fukui, A., & Suzuki, T. K. 2024, ApJ, 973, 128, doi: 10.3847/1538-4357/ad67c9

    2024 doi

  87. [96]

    A., Marchant, P., & Rogers, L

    Valsecchi, F., Rappaport, S., Rasio, F. A., Marchant, P., & Rogers, L. A. 2015, ApJ, 813, 101, doi: 10.1088/0004-637X/813/2/101

    2015 doi

  88. [97]

    2018, MNRAS, 475, 4579, doi: 10.1093/mnras/sty080

    Vidal, J., Cébron, D., Schaeffer, N., & Hollerbach, R. 2018, MNRAS, 475, 4579, doi: 10.1093/mnras/sty080

    2018 doi

  89. [98]

    2022, ApJL, 941, L31, doi: 10.3847/2041-8213/aca47e

    Vissapragada, S., Chontos, A., Greklek-McKeon, M., et al. 2022, ApJL, 941, L31, doi: 10.3847/2041-8213/aca47e

    2022 doi

  90. [99]

    M., Thorngren, D., Lu, T., & Militzer, B

    Wahl, S. M., Thorngren, D., Lu, T., & Militzer, B. 2021, ApJ, 921, 105, doi: 10.3847/1538-4357/ac1a72

    2021 doi

  91. [100]

    2024, ApJS, 270, 14, doi: 10.3847/1538-4365/ad0847

    Wang, W., Zhang, Z., Chen, Z., et al. 2024, ApJS, 270, 14, doi: 10.3847/1538-4365/ad0847

    2024 doi

  92. [101]

    J., & Davis, Leverett, J

    Weber, E. J., & Davis, Leverett, J. 1967, ApJ, 148, 217, doi: 10.1086/149138

    1967 doi

  93. [102]

    N., Arras, P., Quataert, E., & Burkart, J

    Weinberg, N. N., Arras, P., Quataert, E., & Burkart, J. 2012, ApJ, 751, 136, doi: 10.1088/0004-637X/751/2/136

    2012 doi

  94. [103]

    N., Davachi, N., Essick, R., et al

    Weinberg, N. N., Davachi, N., Essick, R., et al. 2024, ApJ, 960, 50, doi: 10.3847/1538-4357/ad05c9

    2024 doi

  95. [104]

    N., Fabrycky, D., Albrecht, S., & Johnson, J

    Winn, J. N., Fabrycky, D., Albrecht, S., & Johnson, J. A. 2010, ApJL, 718, L145, doi: 10.1088/2041-8205/718/2/L145

    2010 doi

  96. [105]

    N., Sanchis-Ojeda, R., & Rappaport, S

    Winn, J. N., Sanchis-Ojeda, R., & Rappaport, S. 2018, NewAR, 83, 37, doi: 10.1016/j.newar.2019.03.006

    2018 doi

  97. [106]

    1991, AJ, 102, 1528, doi: 10.1086/115978

    Wisdom, J., & Holman, M. 1991, AJ, 102, 1528, doi: 10.1086/115978

    1991 doi

  98. [107]

    S., & Ragozzine, D

    Wolf, A. S., & Ragozzine, D. 2009, in IAU Symposium, Vol. 253, Transiting Planets, ed. F. Pont, D. Sasselov, & M. J. Holman, 163–169, doi: 10.1017/S1743921308026367

    2009 doi

  99. [108]

    2022, AJ, 163, 175, doi: 10.3847/1538-3881/ac5680

    Wong, I., Shporer, A., Vissapragada, S., et al. 2022, AJ, 163, 175, doi: 10.3847/1538-3881/ac5680

    2022 doi

  100. [109]

    2021, AJ, 162, 256, doi: 10.3847/1538-3881/ac26bd

    Wong, I., Shporer, A., Zhou, G., et al. 2021, AJ, 162, 256, doi: 10.3847/1538-3881/ac26bd

    2021 doi

  101. [110]

    T., Marcy, G

    Wright, J. T., Marcy, G. W., Howard, A. W., et al. 2012, ApJ, 753, 160, doi: 10.1088/0004-637X/753/2/160

    2012 doi

  102. [111]

    W., Winn, J

    Yee, S. W., Winn, J. N., Knutson, H. A., et al. 2020, ApJL, 888, L5, doi: 10.3847/2041-8213/ab5c16

    2020 doi

  103. [112]

    2024, NewA, 106, 102130, doi: 10.1016/j.newast.2023.102130

    Yeh, L.-C., Jiang, I.-G., & A-thano, N. 2024, NewA, 106, 102130, doi: 10.1016/j.newast.2023.102130

    2024

  104. [113]

    Zahn, J. P. 1989, A&A, 220, 112

    1989

  105. [114]

    Zahn, J. P. 2008, in EAS Publications Series, ed. M. J. Goupil & J. P. Zahn, Vol. 29, 67–90, doi: 10.1051/eas:0829002

    2008 doi

  106. [115]

    Zendejas, J., Segura, A., & Raga, A. C. 2010, Icarus, 210, 539, doi: 10.1016/j.icarus.2010.07.013

    2010 doi

  107. [116]

    N., & Trubitsyn, V

    Zharkov, V. N., & Trubitsyn, V. P. 1978, Physics of planetary interiors

    1978

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